Dynamics of Weakly Localized Electrons in Thin Semiconductor-Copper Sandwiches.

We have investigated the dynamics of electrons in a series of ultra-thin Copper films (sandwiched between protective layers of either Germanium or Silicon) in the weak localization regime. Using a contactless technique, we have measured the changes in the ac conductivity at a fixed microwave frequency (omega ~ 10^{11}_{rm S} ^{-1}) as a function of applied static magnetic field, for different temperatures. By decreasing the temperature below 5 K we can tune the dephasing rate below our measurement frequency, which produces a difference between the real part of the ac magnetoconductivity and the dc magnetoconductivity for small static fields. Corresponding changes occur in the imaginary part of the ac magnetoconductivity as the temperature or magnetic field is varied. We obtain similar results on samples with different thicknesses, and we find that the magnitude of the ac effect remains constant even as we vary the sheet resistance by a factor of three. The magnetoconductivity data for all of our samples can be well-described by frequency-dependent weak localization theory provided that contributions from superconducting (Maki-Thompson) fluctuations are taken into account. We have also directly observed superconducting transitions near 0.4 K for Ge-Cu-Ge samples, and we see strong evidence for superconductivity in the Si-Cu-Si samples, with a transition temperature below 0.3 K. The temperature variation of the dephasing rate, tau_sp{varphi }{-1}, which we extract from the theoretical fits to the dc data, fully confirms the picture that the rates become smaller than omega for temperatures below about 5 K. We find an approximately linear temperature dependence for tau_ varphi(T) below 6 K, which is consistent with theories of enhanced electron-electron inelastic scattering, but the theories do not give the correct magnitude for tau_varphi(T).